Geodesic
An upper bound of a generalized upper Hamiltonian number of a graph
Archivum mathematicum, Tome 57 (2021) no. 5, pp. 299-311.

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In this article we study graphs with ordering of vertices, we define a generalization called a pseudoordering, and for a graph $H$ we define the $H$-Hamiltonian number of a graph $G$. We will show that this concept is a generalization of both the Hamiltonian number and the traceable number. We will prove equivalent characteristics of an isomorphism of graphs $G$ and $H$ using $H$-Hamiltonian number of $G$. Furthermore, we will show that for a fixed number of vertices, each path has a maximal upper $H$-Hamiltonian number, which is a generalization of the same claim for upper Hamiltonian numbers and upper traceable numbers. Finally we will show that for every connected graph $H$ only paths have maximal $H$-Hamiltonian number.
DOI : 10.5817/AM2021-5-299
Classification : 05C12, 05C45
Keywords: graph; vertices; ordering; pseudoordering; upper Hamiltonian number; upper traceable number; upper H-Hamiltonian number; Hamiltonian spectra 
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     title = {An upper bound of a generalized upper {Hamiltonian} number of a graph},
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Dzúrik, Martin. An upper bound of a generalized upper Hamiltonian number of a graph. Archivum mathematicum, Tome 57 (2021) no. 5, pp. 299-311. doi : 10.5817/AM2021-5-299. http://geodesic.mathdoc.fr/articles/10.5817/AM2021-5-299/

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